Comparative study on three-dimensional statistical damage constitutive modified model of rock based on power function and Weibull distribution
Tóm tắt
According to the characteristics of the microscopic unit strength of rock with random distribution, the power function distribution, and the Weibull distribution which is widely used in the past as the distribution function of the strength of the rock. Based on the theory of rock damage and statistical strength theory, two damage constitutive models established under three different confining pressures are modified. Then, the damage constitutive modified model of two kinds of distribution is verified and compared with the existing three axis test data. The results show that: (1) In the stage of elastic deformation of rock, the two theoretical damage constitutive model curves are in high agreement with the three axis test curve; (2) The rock at the plastic stage (hardening and softening), damage constitutive model established by Weibull probability distribution and experimental curve fits better than the damage constitutive model established by power function distribution. Especially in high confining pressure, damage constitutive model based on Weibull distribution can well describe the rock deformation from brittle to ductile transition process and power function is not; (3) In the residual strength in rock, damage variable D of damage constitutive model based on power function distribution appeared more than 1, which is deviation from the actual one and damage constitutive model based on Weibull distribution is not deviating. To summarize, using Weibull distribution statistical probability model to describe the microscopic unit strength of rock is more reasonable.
Tài liệu tham khảo
Cao WG, Li X, Zhao H (2007) Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination. J Cent S Univ Technol 14(5):719–724
Cao WL, Peng XH, Ren ZJ et al (2010) Mesoscopic damage constitutive model of bedded salt rock mass under tri-axial compression. Chin J Rock Mech Eng 29(11):2304–2311
Deng J, Gu DS (2011) On a statistical damage constitutive model for rock materials. Comput Geosci 37(2):122–128
Gao C, Xie LZ, Xie HP, He B, Li CB, Wang J et al (2016) Coupling between the statistical damage model and permeability variation in reservoir sandstone: theoretical analysis and verification. J Nat Gas Sci Eng 37:375–385
Jiang W, Deng J, Li Y (2010) Research on constitutive model of rock damage based on log normal distribution. J Undergr Sp Eng 6(6):1190–1194
Krajcinovic D, Silva MA (1982) Statistical aspects of the continuous damage theory. Int J Solids Struct 18(7):551–562
Lee HK, Simunovic S (2001) A damage constitutive model of progressive debonding in aligned discontinuous fiber composites. Int J Solids Struct 38(5):875–895
Li G, Tang CA (2015) A statistical meso-damage mechanical method for modeling trans-scale progressive failure process of rock. Int J Rock Mech Min Sci 74:133–150
Li SC, Xu J, Tao YQ, Tang XJ (2007) Study on damage constitutive model of rock damage based on lognormal distribution. J Coal Sci Eng 13(4):430–433
Li X, Cao WG, Su YH (2012) A statistical damage constitutive model for softening behavior of rocks. Eng Geol 143–144:1–17
Li TC, Lyu LX, Zhang SL, Sun JC (2015) Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements. J Zhejiang Universityence A 16(8):644–655
Rinaldi A, Lai YC (2007) Statistical damage theory of 2D lattices: energetics and physical foundations of damage parameter. Int J Plast 23(10–11):1796–1825
Wang ZL, Li YC, Wang JG (2007) A damage-softening statistical constitutive model considering rock residual strength. Comput Geosci 33:1–9
Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297
Xie HP, Gao F (2000) The mechanics of cracks and a statistical strength theory for rocks. Int J Rock Mech Min Sci 37:477–488
Xu P, Yang SQ (2017) A fracture damage constitutive model for fissured rock mass and its experimental verification. Arab J Geosci 10(7):164
Xue YL, Lin F, Li SL (2008) Study on compression test and damage constitutive model of rock under different confining pressures. In: Proceedings of the first National Symposium on rock and soil structure theory. pp 79–85
Zeng YW, Zhao ZY, Zhu YW (2002) Bifurcation analysis on failure forms of rock material. Chin J Rock Mechan Eng 21(7):948–952
Zhang M, Wang F, Yang Q (2013) Statistical damage constitutive model of rock based on three axis compression test. Chin J Geotech Eng 35(11):1965–1971